I will give an introduction to differentially large fields (a differential analogue to the notion of large field). I will present some explicit constructions/examples using formal power series (with a focus on constructing differentially closed fields). I will then recall the notion of PAC-differential field (relating them to differentially large fields) and present examples arising from finite groups acting by differential automorphisms. Time permitting, we will see an overview of the model-theoretic properties of PAC-differential fields that are bounded as fields (translating work of Hrushovski, Chatzidakis-Pillay to the differential context). This is (separate) joint work with M. Tressl and D. Hoffmann.